I agree with bugsbunny. Aakash has to fulfill the contract. He is paid to cover Arjun. Without going with Arjun how will he shoot Arjun.
I would say this is the real test for Aakash-Anjali. It is not because he doesn't love her he tells that, but he is having no other option at this point. He will not intentionally hurt her.
It is more like colonel's decision to leave Anjali at base camp. If it was protective instinct for a girl then, it is call of duty now.
I love this show because it not only concentrates on diemmas of a girl, it also concentrates on the dilemma's faced by guys too.
Already we saw how family pressure is kept on Vidhaan to do a marriage he def does not want to do and wants to back out at the right time. So this is another dilemma for Aakash, between duty and love.
He chooses duty. what is wrong in it. If he allows Anjali to go what about his future as there is every chance he wont get such a plum assignment whereas Anjali after summiting Everest is gonna go with her life with Vidhaan.
Being a obedient daughter to Jagat is important to Anjali even that means not hearing her heart's call, so Aakash is perfectly fine if he requests Anjali to stay in camp 4 for his duty.